Question

How do you find the indefinite integral of ∫ (x - sinx ) dx / x^2 + 2 cosx ?

Answer 1

`I=1/2ln(x^2+2cos(x))+C`

Explanation:

We want to solve

`I=int(x-sin(x))/(x^2+2cos(x))dx`

Make a substitution
`color(red)(u=x^2+2cos(x)=>du=2x-2sin(x)=2(x-sin(x))dx`

`I=1/2int1/udu`

`color(white)(I)=1/2ln(u)+C`

`color(white)(I)=1/2ln(x^2+2cos(x))+C`